Envelope solution profiles of the discrete nonlinear Schrِdinger equation with a saturable nonlinearity

In this Letter, the discrete nonlinear Schrِdinger equation with a saturable nonlinearity is investigated via the extended Jacobi elliptic function expansion method. As a consequence, with the aid of symbolic computation, a variety of new envelope periodic wave solutions are obtained in terms of Jacobi elliptic functions. In particular, the discrete dark soliton solution is also given. We analyze the structures of some of the obtained solutions via the figures.